arXiv subjects

M. Requardt

Publications and source records attributed to M. Requardt.

4 recordsLinked to original sources

arXiv2008

About the Minimal Resolution of Space-Time Grains in Experimental Quantum Gravity

We critically analyse and compare various recent thought experiments, performed by Amelino-Camelia, Ng et al., Baez et al., Adler et al., and ourselves, concerning the (thought)experimental accessibility of the Planck scale by space-time measurements. We show that a closer inspection of the working of the measuring devices, by taking their microscopic quantum many-body nature in due account, leads to deeper insights concerning the extreme limits of the precision of space-time measurements. Among other things, we show how certain constraints like e.g. the Schwarzschild constraint can be circumvented and that quantum fluctuations being present in the measuring devices can be reduced by designing more intelligent measuring instruments. Consequences for various phenomenological quantum gravity models are discussed.

gr-qc↗

arXiv2007

The Statistical Mechanics of Microscopic Long-Range Bulk-Boundary Dependence in Black-Hole Physics and Holography

We argue in the following that the entropy-area law of black-hole physics and the various holographic bounds are the consequences of the microscopic dynamics of elementary degrees of freedom living on or near the Planck scale. We locate them both in the interior and on the boundary of, for example, the black hole with the strange area-behavior of various quantities being the result of a long-range bulk-boundary dependence among these degrees of freedom. In contrast to other approaches we regard the vacuum fluctuations on microscopic scales as the relevant elementary building blocks. In so far certain relations to to old ideas of Sakharov, Zeldovich et al are acknowledged (induced gravity). Most importantly, we prove that the existence of a large energy gap between a few low-lying excitation patterns and the majority of the other (in principle) possible excitation patterns in a subvolume with given boundary excitation is crucial for this area-dependence. We also remark that this is an indication that some particular entangled space-time geometry of a somewhat non-local character prevails in the microscopic (Planck) regime. Our findings are corroborated by the explanation of a number of open questions in the field (see the table of contents at the end of the introduction).

hep-th↗

arXiv1997

A New Approach to Functional Analysis on Graphs, the Connes-Spectral Triple and its Distance Function

Continuing previous work we develop a certain piece of functional analysis on general graphs and use it to create what Connes calls a 'spectral triple', i.e. a Hilbert space structure, a representation of a certain (function) algebra and a socalled 'Dirac operator', encoding part of the geometric/algebraic properties of the graph. We derive in particular an explicit expression for the 'Connes-distance function' and show that it is in general bounded from above by the ordinary distance on graphs (being, typically, strictly smaller(!) than the latter). We exhibit, among other things, the underlying reason for this phenomenon.

hep-th↗

arXiv1995

Discrete Mathematics and Physics on the Planck-Scale

Starting from the hypothesis that both physics, in particular space-time and the physical vacuum, and the corresponding mathematics are discrete on the Planck scale we develop a certain framework in form of a '{\it cellular network}' consisting of cells interacting with each other via bonds. Both the internal states of the cells and the "strength" of the bonds are assumed to be dynamical variables. In section 3 the basis is laid for a version of '{\it discrete analysis}' which, starting from different, perhaps more physically oriented principles, manages to make contact with the much more abstract machinery of Connes et al. and may complement the latter approach. In section 4 a, as far as we can see, new concept of '{\it topological dimension}' in form of a '{\it degree of connectivity}' for graphs, networks and the like is developed. It is then indicated how this '{\it dimension}', which for continuous structures or lattices being embedded in a continuous background agrees with the usual notion of dimension, may change dynamically as a result of a '{\it phase transition like}' change in '{\it connectivity}' in the network. A certain speculative argument, along the lines of statistical mechanics, is supplied in favor of the naturalness of dimension 4 of ordinary (classical) space-time.

hep-th↗